Abstract
The sideways heat equation is considered in terms of the ill-posed operator equation Au = g, g ∈ R(A) ⊂ L2(ℝ), with a given noisy right hand side. For a reconstruction of the solution from indirect data the dual least square method generated by the family of Meyer wavelet subspaces is applied. An explicit relation between the truncation level of the wavelet expansion and the data error bound is found under which convergence results including error estimation are obtained. Next, a certain simple nonlinear modification of the method based on local refinements of the wavelet expansion of the noisy data is investigated. Moreover, it is shown that an accuracy of the solution reconstruction can be improved by adding some sufficiently large coefficients on the level higher than that indicated by the convergence theorem.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
